Question

skill set #3.5 - angle relationships with parallel lines
given ( m parallel n ), find the value of x.
answer attempt 1 out of 5
( x = )

Explanation:

Step1: Use the property of alternate interior angles

Since \(m\parallel n\), the angle \((3x + 7)^{\circ}\) and the angle \((x+19)^{\circ}\) are alternate interior angles. Alternate interior angles are equal. So, \(3x + 7=x + 19\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(3x-x+7=x - x+19\), which simplifies to \(2x+7 = 19\).
Subtract \(7\) from both sides: \(2x+7-7=19 - 7\), so \(2x=12\).
Divide both sides by \(2\): \(x=\frac{12}{2}\).

Answer:

\(6\)